# How to generate a Penrose tessellation around a given tile?

Given a starting Penrose tile, I need to build a "spiraling" tessellation around it.

The following picture illustrates the request:

In this example, the starting tile is a "thin rhombus" (the pink one).

I need to write an algorithm which is able to generate the $$n$$ tiles (and whose output is, for instance a, SVG file), starting from any given tile, and with the possibility of coloring the tiles according to a given sequence of $$n$$ colors.

Thanks for your help!

NOTE: This post is related to this one.

• From a graph-point-of-view, you are traversing the dual-graph of the tiling, with the convention of taking the right-most turn each time. – Alex R. Sep 10 '18 at 19:07
• @AlexR. The dual graph is the network of the centers of the tiles, right? In this case, the problem becomes how to predict the $n$-th center, right? – user559615 Sep 10 '18 at 19:11
• How is your penrose tiling stored? – Alex R. Sep 10 '18 at 20:46
• So far I made a Xfig file (mcj.sourceforge.net), which can be easily transformed into a SVG file and viceversa, perhaps more common. In practice, for each tile I have 4 points. But I'm not sure it is the best way to store it. – user559615 Sep 10 '18 at 21:10
• Say, I would prefer not to store the underlying Penrose tiling, but to generate the next tile from first principles, a bit as i tried to depict in the figure above. – user559615 Sep 10 '18 at 21:16